I purchased and installed the Lr6 upgrade (I have been using Lr 5.7). However, during the upgrade process a message flashed up that no other installed version of the software could be found and asked me to input the serial number of my previous copy, which I did, assuming that it would install as an upgrade.

However, what has happened is that Lr6 has installed a trial version of Lr6, and I can see no way of changing this other than to purchase the cc version. Both Lr5 and 6 now run on my machine without any apparent problems.

Is there no option other than to uninstall and re-install? Will anything be solved in the Lr6 upgrade again fails to see the copy of Lr5?

Did not work for me. After signing out and re-launching LR, I'm prompted to sign in as in step 2 but but after I click "Sign in Now" it does not give me any choice to license, goes directly to the Adobe sign in prompt, already filled in with my user name.

So in this case you have to 'simply' create a new Adobe ID, one without a CC account, even a trail CC account, associated. So now I have to create a new email account to create a new Adobe ID to register LR6.